51* Mr. S. Beswick 07i a Method for 



(10.) Correct for the earth's rotundity in longitude. At a 

 distance of" 90° from each pole all angles vanish ; I therefore 

 take the least and greatest distances of the magnetic pole, and 

 proceed in a duplicate ratio, taking 90° as a basis, thus: 

 70°2: 110°:: 51° 29°-^: 59° 30': 



which is the same as saying, as the square of the least distance 

 of the magnetic pole is to the greatest distance, so is the square 

 of the latitude of Greenwich to the number required. 



This number must be adapted to the angle of longitude by 

 the correcting nuniber in the middle clause of item ninth. 



90° : 59° 30' : : 2"^ 28' : 1° 37'. 



This number is used for the correction of longitude ; thus, 

 m the present case, 



91°-1°37'=89°23'. 



(11.) Having made these corrections, now obtain the tri- 

 gonometrical values of the side and angle, be and boa. 



First find the side dc, thus : as the radius is to the sine ac 

 (38^ 31'), so is the sine dac (89° 23') to the sine dc, or thus : 



sine 38° 31' . . . . 9794-31 

 sine 89° 23' .... 999997 



sine 38° 31' ... . 979428 



Find the side da, as follows: as the tangent to the comple- 

 ment ac (38° 31') is to the whole sine, so is the sine of the 

 complement cad (89° 23') to the tangent ad (29') j or thus : 



sine of comp. and rad. 8.9° 23' . . 1803194 

 tang, to comp. . . 33° 31' . . 1009914 



tan 29' . . 793280 



The side be may now be found in the following manner. 

 Obtain bd by adding ba and ad, thus : 



22° 28' + 29' = 22° 57'; 

 then be results from the following proportion : as the radius 

 is to the sine of the complement dc (38° 31'), so is the sine of 

 the complement db (22° 57') to the sine of the complement be 

 (43° 54'). Or logarithmically thus : 



sine to comp. 38° 31' . . . . 989344 

 sine to comp. 22° 57' .... 996419 



sine to comp. 43° 54' ... . 985763 

 This is the value of the side be. 



(12.) Now find the angle bca, thus : as the sine be is to the 

 sine bac, so is the sine ba to the sine bea. Or thus : 



